The girl with her months-old baby, her mother and her brother, were led to a meeting with the president by the governor of Borno state, Kashim Shettima, Xinhua reported.
Ali-Nkeki was the first Chibok girl to be rescued by Nigerian authorities.
A total of 276 girls were abducted by Boko Haram militants from their secondary school dormitories in Chibok town in the northeastern Borno state in April 2014.
About 57 girls managed to escape later, but more than 200 remain missing.
President Buhari had a closed-door meeting with the Shettima and Ali-Nkeki. The girl and her baby were shielded from journalists by security officers.
An army spokesperson on Wednesday said Ali-Nkeki was among a group of people rescued by Nigerian troops at Baale community in Borno state.
Sources said Ali-Nkeki was rescued in the Sambisa Forest on Sunday by the Nigeria army.